OBTAINING OPTIMAL PARETO SOLUTIONS USING A HYBRID APPROACH COMBINING ε-CONSTRAINT AND MOMA-PLUS METHOD

---

Résumé

In this paper, we propose a new hybrid technique for nonlinear multi-objective optimization problems. This method combines the ε-constraint approach with the MOMA-Plus method. This involves using the ε-constraint technique to transform the initial problem into a single-objective one, instead of an aggregation function. The use of these functions of aggregation, in the MOMA-Plus algorithm, requires that weights be fixed in advance by objective functions. For multi- objective problems, the resulting objective function becomes hard to optimize because it is a combination of all objective functions. This is because of the aggregation parameters. Our method allows the use of fewer parameters, and the final objective function to optimize is simpler. To demonstrate the performance of our method, we examined height test problems and computed three performance indexes. The results allow us to compare our method to the other one. The goodness of the convergence and diversity of Pareto optimal solutions prove that our method is the best choice for multi-objective optimization problems.

Mots-clés

Mathematical optimization, Pareto principle, Constraint (computer-aided design), Pareto optimal, Computer science, Mathematics, Multi-objective optimization